Effects of eddy currents in transformer windings
01 Aug 1966-Vol. 113, Iss: 8, pp 1387-1394
TL;DR: In this article, the effect of eddy currents on transformer windings is considered and a method is derived for calculating the variation of winding resistance and leakage inductance with frequency for transformers with single-layer, multilayer and sectionalised windings.
Abstract: The effects of eddy currents in transformer windings are considered, and a method is derived for calculating the variation of winding resistance and leakage inductance with frequency for transformers with single-layer, multilayer and sectionalised windings. The method consists in dividing the winding into portions, calculating the d.c. resistances and d.c. leakage inductances of each of these portions, and then multiplying the d.c. values by appropriate factors to obtain the corresponding a.c. values. These a.c. values are then referred to, say, the primary winding and summed to give the total winding resistance and leakage inductance of the transformer. Formulas are derived and quoted for calculating the d.c. resistances and leakage inductances of the winding portions. Theoretical expressions are derived for the variation with frequency etc. of the factors by which the d.c. values must be multiplied to obtain the corresponding a.c. values. These expressions are presented in the form of graphs, permitting the factors to be read as required.
Citations
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TL;DR: In this paper, the authors compared several expressions for high-frequency winding resistance of inductors and compared the theoretical predictions calculated from these expressions with experimental results, and identified the expressions that yield the most accurate prediction of the winding highfrequency resistance.
Abstract: The paper reviews several expressions for high-frequency winding resistance of inductors proposed by several authors and compares the theoretical predictions calculated from these expressions with experimental results. It identifies the expressions that yield the most accurate prediction of the winding high-frequency resistance. The comparison shows that the method proposed by Dowell (1966) accurately predicts the AC resistance if the winding contains less than three layers. The methods proposed by several other authors accurately predict the high-frequency resistance only in certain frequency ranges. In addition, these expressions yield inaccurate results for the inductor quality factor. One expression, however, accurately predicts both the high-frequency winding resistance and the quality factor of inductors over a wide frequency range from the DC to the first resonant frequency. The paper concludes with a simple and accurate circuit model describing the frequency behavior of inductors.
167 citations
17 May 2009
TL;DR: In this article, the maximum attainable efficiency and the dependency of the efficiency limit on technological parameters are determined for single-phase PFC boost rectifiers, and a comprehensive numerical efficiency optimization is carried out which identifies an efficiency limit of 99.2% for a 3.2kW system.
Abstract: Up to now, in the development of power electronics systems, the reduction of the initial costs or the increase of the power density have been of primary concern. However, with increasing energy costs also the power conversion efficiency is gaining higher and higher importance. Accordingly, while maintaining high power density, an efficiency as high as possible must be obtained. In this paper the maximum attainable efficiency and the dependency of the efficiency limit on technological parameters is determined for single-phase PFC boost rectifiers. In a first step basic PFC boost rectifier topologies are briefly compared with regard to high efficiency and a dual-boost PFC rectifier with integral common-mode filtering is selected as basis for the investigations. Next, simple approximations of the technological limits of the system performance are calculated in the efficiencypower density plane. With this, the Feasible Performance Space and the reduction in power density which has to be accepted for increasing the efficiency are clarified, and the trade-off limit curve (Pareto Front) of a multi-objective, i.e. efficiency and power density design optimization is determined. Furthermore, a comprehensive numerical efficiency optimization is carried out which identifies an efficiency limit of 99.2% for a 3.2kW system. The theoretical considerations are verified by experimental results from a laboratory prototype of the ultra-high efficiency system achieving 99.1% efficiency at a power density of 1.1kW/din3, as well as those firom an ultra-compact dual-boost PFC rectifier (95.8%, 5.5kW/dn3) and a very low switching freluency (3kHz) conventional PFC boost rectifier (96.7%, 2kW/din3). Finally, the sensitivity of the efficiency optimum with regard to various technological parameters is analyzed and an outlook on the further course of the research is given.
154 citations
TL;DR: In this paper, the design graphs and design examples for 10 MHz transformers are presented, as well as design examples of 10 GHz transformers with fine patterning produced by photolithography.
Abstract: Transformers and inductors fabricated with micron-scale magnetic-alloy and copper thin films are designed for high-frequency power conversion applications. Fine patterning produced by photolithography reduces eddy current losses, thus enabling very high power densities. Calculated design graphs and design examples for 10 MHz transformers are presented.
152 citations
TL;DR: In this paper, a 1-MHz 1-kW LLC resonant converter using GaN devices and planar matrix transformers is proposed for data center data center applications, which achieves high-current, high-efficiency, and low-cost power solutions.
Abstract: Data centers demand high-current, high-efficiency, and low-cost power solutions. The high-voltage dc distribution power architecture has been drawing attention due to its lower conduction loss on cables and harnesses. In this structure, the 380–12 V high output current isolated converter is the key stage. This paper presents a 1-MHz 1-kW LLC resonant converter using GaN devices and planar matrix transformers that are designed and optimized for this application. The transformer design and the optimization of the output capacitor termination are performed and verified. Finally, this cost-effective converter achieves above 97% peak efficiency and 700-W/in $^{{{3}}}$ power density.
151 citations
TL;DR: In this paper, a bidirectional isolated dc-dc converter controlled by phase-shift angle and duty cycle for the fuel-cell hybrid energy system is analyzed and designed, which minimizes the number of switches and their associated gate driver components by using two high-frequency transformers that combine a half-bridge circuit and a fullbridge circuit together on the primary side.
Abstract: Electrical power systems in future uninterruptible power supplies or electrical vehicles may employ hybrid energy sources, such as fuel cells and supercapacitors. It will be necessary to efficiently draw the energy from these two sources as well as recharge the energy storage elements by the dc bus. In this paper, a bidirectional isolated dc-dc converter controlled by phase-shift angle and duty cycle for the fuel-cell hybrid energy system is analyzed and designed. The proposed topology minimizes the number of switches and their associated gate driver components by using two high-frequency transformers that combine a half-bridge circuit and a full-bridge circuit together on the primary side. The voltage doubler circuit is employed on the secondary side. The current-fed input can limit the input current ripple that is favorable for fuel cells. The parasitic capacitance of the switches is used for zero voltage switching (ZVS). Moreover, a phase-shift and duty-cycle modulation method is utilized to control the bidirectional power flow flexibly and it also makes the converter operate under a quasi-optimal condition over a wide input voltage range. This paper describes the operation principle of the proposed converter, the ZVS conditions, and the quasi-optimal design in depth. The design guidelines and considerations regarding the transformers and other key components are given. Finally, a 1-kW 30~50-V-input 400-V-output laboratory prototype operating at 100-kHz switching frequency is built and tested to verify the effectiveness of the presented converter.
150 citations
References
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TL;DR: In this article, a multilayer winding carrying an alternating current, such as the windings illustrated in figures 1, 2, and 3, each layer of copper lies in the alternating magnetic field set up by the current in all the other layers.
Abstract: IN any multilayer winding carrying an alternating current, such as the windings illustrated in figures 1, 2, and 3, each layer of copper lies in the alternating magnetic field set up by the current in all the other layers. Eddy currents are set up in each layer in a direction to partly neutralize the magnetic intensities in the interior of the copper wire in each layer. As a result of the eddy-current losses in the copper, the effective resistance of the winding to the alternating current it carries may be many times its resistance to continuous currents.
103 citations
TL;DR: In this article, the authors discuss the more important causes of eddy currents in heavy conductors carrying alternating currents and surrounded on three sides by iron, and propose a method to identify the most important causes.
Abstract: The object of the present paper is the discussion of the more important causes of eddy currents in heavy conductors carrying alternating currents and surrounded on three sides by iron.
93 citations
64 citations
TL;DR: In this article, it is shown that a considerable proportion of the effective resistance of inductive coils when used at radio frequencies is caused by the eddy-currents set up in the wires of the coils by the alternating magnetic field in which they are situated, and that in extreme cases the alternating current resistance may amount to more than one hundred times the direct current resistance.
Abstract: It is well-known that a considerable proportion of the effective resistance of inductive coils when used at radio frequencies is caused by the eddy-currents set up in the wires of the coils by the alternating magnetic field in which they are situated, and that in extreme cases the alternating current resistance may amount to more than one hundred times the direct current resistance. It is therefore important to have reliable formulae for the eddy-current resistance of such coils in order to determine the conditions which will reduce the eddy-current losses to a minimum. The simplest case, that of a long straight cylindrical wire under the action of its own current, has been treated by Kelvin, Rayleigh, Heaviside, and others. The general effect is known as the “skin effect,” because the current tends to concentrate more and more upon the skin of the conductor as the frequency increases.
49 citations
TL;DR: In this article, the authors show how hyperbolic functions of complex angles may be applied to the solution of the problem of heat losses in rectangular conductors that are embedded in open slots.
Abstract: The principal object of this paper is to show how hyperbolic functions of complex angles may be applied to the solution of the problem of heat losses in rectangular conductors that are embedded in open slots. A certain knowledge of the functions themselves is presupposed. Inasmuch, however, as they are handled like trigometric functions of real angles?except in regard to the plus and minus signs?it is a simple matter to acquire the requisite technical skill to use them. The hyperbolic function of a complex angle, consisting as it does of a real and an imaginary part, may represent a vector?the real part being the component of the vector along the horizontal, and the imaginary part, component along the vertical. Thus, for example, A sinh (x + j x) represents a vector just as A e j ? A/?, A (cos ? + j sin ?) represent vectors. Considerable experience has shown that the vector method for handling a-c. problems is much superior to the original method in which simple trigonometric functions were used. With this lesson before us, it should require but little contact with the problem at hand to demonstrate the superiority of the vector method, even though it employs the possibly unfamiliar hyperbolic quantities. These hyperbolic vectors have been used for a number of years in the analysis of problems involving a-c. circuits, which have distributed inductance and capacitance, and have proved their usefulness.
27 citations